What Trigonometry is good for!

Seriously, I have to be the weirdest college student ever. I tutor college math, I run a business, I love science, and I read books. Sorry for the sarcasm but interacting with my peers on a daily basis does little to give me hope for the future of society. Anyway, on to the nerdy subject of math, of course I found a way to use trig for horse stuff...

In the spring I took a trigonometry class and yesterday I applied it to the barrel pattern. In barrel racing, the barrels are set up in a triangle, with 90 feet between the first two and 105 feet between the third and the other two (for a standard pattern, there are others). Ever wonder what the degree of the angles between the barrels are? Probably not, but I did. With a barrel pattern you have the 3 sides known but no angles.
So I used the law of cosines equation to derive the angle, below:



It turns out that the angle at the first two barrels is 64.62 degrees, and the third is 50.76.


I was curious if the "small" 60 X 90 barrel pattern would have the same angles as the standard, but it doesn't. The two large angles are 70.53 degrees and the small is 38.9 degrees.




Thus, the smaller pattern will require the horse to turn tighter around the first and second barrel than a standard because the angle to the third is much steeper.

And you thought math was boring... :D